Symmetry in chemistry from the hydrogen atom to proteins.

The last 2 decades have seen discoveries in highly excited states of atoms and molecules of phenomena that are qualitatively different from the "planetary" model of the atom, and the near-rigid model of molecules, characteristic of these systems in their low-energy states. A unified view is emerging in terms of approximate dynamical symmetry principles. Highly excited states of two-electron atoms display "molecular" behavior of a nonrigid linear structure undergoing collective rotation and vibration. Highly excited states of molecules described in the "standard molecular model" display normal mode couplings, which induce bifurcations on the route to molecular chaos. New approaches such as rigid-nonrigid correlation, vibrons, and quantum groups suggest a unified view of collective electronic motion in atoms and nuclear motion in molecules.

Algebraic methods in spectroscopy.

At present, two main types of algebraic methods are employed for analysis of molecular spectra. The first goes back to the early days of molecular spectroscopy. The second, developed recently by Iachello and coworkers, grew out of nuclear physics and makes use of classical Lie algebras such as SU(4). In this review, the standard spectroscopic fitting Hamiltonian for molecular vibrations, including resonance interactions, is first described. Then, new developments in the application of the standard approach are surveyed. In particular, the question of how one determines the true nature of molecular motions in highly excited spectra is investigated. Next, the recent algebraic approach of Iachello and coworkers is discussed. Application of ideas of molecule-like modes and algebraic methods to the analysis of the electronic spectra of atoms is discussed. Finally, prospects for future development of algebraic methods are discussed.